This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and Sylvester monoids. For Chinese monoids, we first give new presentations via finite complete rewriting systems, using more lucid constructions and proofs than those given independently by Chen & Qui and Güzel Karpuz; we then ...

languages usually involves proving a decomposition theorem. Not only is such a proof tedious, un-inspiring, and error-prone, but also it is usually attempted many times during the design of a theory. With an eye towards automation, we develop an algorithm for checking the statement of the decomposition theorem. Our algorithm is expressed as a sound and complete term rewriting system with respec...

We show that the following (equivalent) problems are P-complete: 1. Does a given connuent NCE graph grammar only generate graphs of bounded tree-width? and 2. is the graph language generated by a given connuent NCE graph grammar an HR language? This settles the complexity of these important problems on graph grammars .

We present a new declarative compilation of logic programs with constraints into variable-free relational theories which are then executed by rewriting. This translation provides an algebraic formulation of the abstract syntax of logic programs. Management of logic variables, unification, and renaming apart is completely elided in favor of algebraic manipulation of variable-free relation expres...

The fundamental groups of most (conjecturally, all) closed 3manifolds with uniform geometries have finite complete rewriting systems. The fundamental groups of a large class of amalgams of circle bundles also have finite complete rewriting systems. The general case remains open.

The completeness (i.e. confluent and terminating) property is an important concept when using a term rewriting system (TRS) as a computational model of functional programming languages. Knuth and Bendix have proposed a procedure known as the KB procedure for generating a complete TRS. A TRS cannot, however, directly handle higher-order functions that are widely used in functional programming la...

We show how the paradigm of learning-based testing (LBT) can be applied to automate speci cation-based black-box testing of reactive systems using term rewriting technology. A general model for a reactive system can be given by an extended Mealy automata (EMA) over an abstract data type (ADT). A nite state EMA over an ADT can be e ciently learned in polynomial time using the CGE regular inferen...

This paper discusses determinization of conditional term rewriting systems with oriented constructor rules. We present a rule-based transformation system, which transforms a non-deterministic one into a deterministic one, together with examples of the transformation. We prove that the transformation system is simulation sound and simulation complete. We also prove that the transformation system...

Model checking of recursion schemes, known as higher-order model checking, has actively been studied recently and is becoming a basis for verification of higher-order programs. Some practical model checking algorithms have been developed based on the reduction from model checking to intersection type inference, but they are not completely satisfactory. We propose a novel approach to developing ...